Slope of Channel given Discharge per Unit Channel Width Solution

STEP 0: Pre-Calculation Summary
Formula Used
Slope of bed = (3*Dynamic Viscosity*Discharge per Unit Width)/(Specific Weight of Liquid*Diameter of Section^3)
i = (3*μviscosity*q)/(γf*dsection^3)
This formula uses 5 Variables
Variables Used
Slope of bed - The Slope of bed is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow.
Dynamic Viscosity - (Measured in Pascal Second) - The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.
Discharge per Unit Width - (Measured in Square Meter per Second) - The Discharge per Unit Width is the ratio of total discharge in the channel to the width considered.
Specific Weight of Liquid - (Measured in Newton per Cubic Meter) - Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid.
Diameter of Section - (Measured in Meter) - Diameter of Section is the diameter of the circular cross-section of the beam.
STEP 1: Convert Input(s) to Base Unit
Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Discharge per Unit Width: 10.02 Square Meter per Second --> 10.02 Square Meter per Second No Conversion Required
Specific Weight of Liquid: 9.81 Kilonewton per Cubic Meter --> 9810 Newton per Cubic Meter (Check conversion here)
Diameter of Section: 5 Meter --> 5 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
i = (3*μviscosity*q)/(γf*dsection^3) --> (3*1.02*10.02)/(9810*5^3)
Evaluating ... ...
i = 2.50040366972477E-05
STEP 3: Convert Result to Output's Unit
2.50040366972477E-05 --> No Conversion Required
FINAL ANSWER
2.50040366972477E-05 2.5E-5 <-- Slope of bed
(Calculation completed in 00.019 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal
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18 Laminar Flow of Fluid in an Open Channel Calculators

Slope of Channel given Mean Velocity of Flow
Go Slope of Surface of Constant Pressure = (Dynamic Viscosity*Mean Velocity)/((Diameter of Section*Horizontal Distance-(Horizontal Distance^2)/2)*Specific Weight of Liquid)
Diameter of Section given Mean Velocity of Flow
Go Diameter of Section = ((Horizontal Distance^2+(-Dynamic Viscosity*Mean Velocity*Slope of Surface of Constant Pressure/Specific Weight of Liquid)))/Horizontal Distance
Mean Velocity in flow
Go Mean Velocity = -(Specific Weight of Liquid*Piezometric Gradient*(Diameter of Section*Horizontal Distance-Horizontal Distance^2))/Dynamic Viscosity
Dynamic Viscosity given Mean Velocity of Flow in Section
Go Dynamic Viscosity = (Specific Weight of Liquid*Piezometric Gradient*(Diameter of Section*Horizontal Distance-Horizontal Distance^2))/Mean Velocity
Diameter of Section given Potential Head Drop
Go Diameter of Section = sqrt((3*Dynamic Viscosity*Mean Velocity*Length of Pipe)/(Specific Weight of Liquid*Head Loss due to Friction))
Length of Pipe given Potential Head Drop
Go Length of Pipe = (Head Loss due to Friction*Specific Weight of Liquid*(Diameter of Section^2))/(3*Dynamic Viscosity*Mean Velocity)
Potential Head Drop
Go Head Loss due to Friction = (3*Dynamic Viscosity*Mean Velocity*Length of Pipe)/(Specific Weight of Liquid*Diameter of Section^2)
Diameter of Section given Discharge per Unit Channel Width
Go Diameter of Section = ((3*Dynamic Viscosity*Discharge per Unit Width)/(Slope of bed*Specific Weight of Liquid))^(1/3)
Dynamic Viscosity given Discharge per Unit Channel Width
Go Dynamic Viscosity = (Specific Weight of Liquid*Slope of bed*Diameter of Section^3)/(3*Discharge per Unit Width)
Slope of Channel given Discharge per Unit Channel Width
Go Slope of bed = (3*Dynamic Viscosity*Discharge per Unit Width)/(Specific Weight of Liquid*Diameter of Section^3)
Discharge per unit channel width
Go Discharge per Unit Width = (Specific Weight of Liquid*Slope of bed*Diameter of Section^3)/(3*Dynamic Viscosity)
Slope of Channel given Shear Stress
Go Bed Slope = Shear Stress/(Specific Weight of Liquid*(Overall diameter of section-Horizontal Distance))
Diameter of Section given Slope of Channel
Go Diameter of Section = (Shear Stress/(Bed Slope*Specific Weight of Liquid))+Horizontal Distance
Horizontal Distance given Slope of Channel
Go Horizontal Distance = Diameter of Section-(Shear Stress/(Bed Slope*Specific Weight of Liquid))
Shear Stress given Slope of Channel
Go Shear Stress = Specific Weight of Liquid*Bed Slope*(Depth-Horizontal Distance)
Diameter of Section given Bed Shear Stress
Go Diameter of Section = Shear Stress/(Bed Slope*Specific Weight of Liquid)
Bed Slope given Bed Shear Stress
Go Bed Slope = Shear Stress/(Diameter of Section*Specific Weight of Liquid)
Bed Shear Stress
Go Shear Stress = Specific Weight of Liquid*Bed Slope*Diameter of Section

Slope of Channel given Discharge per Unit Channel Width Formula

Slope of bed = (3*Dynamic Viscosity*Discharge per Unit Width)/(Specific Weight of Liquid*Diameter of Section^3)
i = (3*μviscosity*q)/(γf*dsection^3)

What is Channel Gradient?

The Channel Gradient is a fundamental parameter in the geomorphologic characterization of river systems; it is a reflection of the changes in the longitudinal sequence of a river through the presence of waterfalls, step pools (fasts and pools), riffle pools (rapids and pools), etc., which makes it a discriminating.

How to Calculate Slope of Channel given Discharge per Unit Channel Width?

Slope of Channel given Discharge per Unit Channel Width calculator uses Slope of bed = (3*Dynamic Viscosity*Discharge per Unit Width)/(Specific Weight of Liquid*Diameter of Section^3) to calculate the Slope of bed, The Slope of Channel given Discharge per Unit Channel Width is defined as the rate at which head of the channel is changing with respect to horizontal line. Slope of bed is denoted by i symbol.

How to calculate Slope of Channel given Discharge per Unit Channel Width using this online calculator? To use this online calculator for Slope of Channel given Discharge per Unit Channel Width, enter Dynamic Viscosity viscosity), Discharge per Unit Width (q), Specific Weight of Liquid f) & Diameter of Section (dsection) and hit the calculate button. Here is how the Slope of Channel given Discharge per Unit Channel Width calculation can be explained with given input values -> 2.5E-5 = (3*1.02*10.02)/(9810*5^3).

FAQ

What is Slope of Channel given Discharge per Unit Channel Width?
The Slope of Channel given Discharge per Unit Channel Width is defined as the rate at which head of the channel is changing with respect to horizontal line and is represented as i = (3*μviscosity*q)/(γf*dsection^3) or Slope of bed = (3*Dynamic Viscosity*Discharge per Unit Width)/(Specific Weight of Liquid*Diameter of Section^3). The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, The Discharge per Unit Width is the ratio of total discharge in the channel to the width considered, Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid & Diameter of Section is the diameter of the circular cross-section of the beam.
How to calculate Slope of Channel given Discharge per Unit Channel Width?
The Slope of Channel given Discharge per Unit Channel Width is defined as the rate at which head of the channel is changing with respect to horizontal line is calculated using Slope of bed = (3*Dynamic Viscosity*Discharge per Unit Width)/(Specific Weight of Liquid*Diameter of Section^3). To calculate Slope of Channel given Discharge per Unit Channel Width, you need Dynamic Viscosity viscosity), Discharge per Unit Width (q), Specific Weight of Liquid f) & Diameter of Section (dsection). With our tool, you need to enter the respective value for Dynamic Viscosity, Discharge per Unit Width, Specific Weight of Liquid & Diameter of Section and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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